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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 4592.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4592.l1 | 4592f2 | \([0, 0, 0, -153781003, 734010288314]\) | \(98191033604529537629349729/10906239337336\) | \(44671956325728256\) | \([]\) | \(592704\) | \(3.0639\) | |
| 4592.l2 | 4592f1 | \([0, 0, 0, -309643, -61048006]\) | \(801581275315909089/70810888830976\) | \(290041400651677696\) | \([]\) | \(84672\) | \(2.0909\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4592.l have rank \(0\).
Complex multiplication
The elliptic curves in class 4592.l do not have complex multiplication.Modular form 4592.2.a.l
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
